Equilibrium, Gravitation and Periodic Motion

Conditions for equilibrium and Elastic Moduli

•  The sum of all forces present in the x, y, and z directions are each distinctly equal to zero.

•  The sum of all torques for any given point are equal to zero.

Elastic moduli (stretching in one, two, and three dimensions)

Sheer stress and strain •  Take your textbook and push on the top cover while the rest

remains on a tabletop. Notice the angular distortion.

Newton’s Law of Gravitation

•  The gravitational force is always attractive and depends on both the masses of the bodies involved and their separations.

Gravitational force changes densities below sea level

•  Just as it’s interesting to remember that all gravitational forces are calculated from the center of the planet, it’s interesting to follow the density as one proceeds from crust to mantle to core.

Gravitational potential energy •  Objects changing their distance from earth are also

changing their potential energy with respect to earth.

Satellite motion

Consider satellite orbits •  Several images of things in orbit to consider are shown below.

A visit to a black hole

Simple harmonic motion: •  An ideal spring responds

to stretch and compression linearly, obeying Hooke’s Law.

•  For a real spring, Hookes’ Law is a good approximation.

Simple harmonic motion viewed as a projection

•  If you illuminate uniform circular motion (say by shining a flashlight on a candle placed on a rotating lazy-Susan spice rack), the shadow projection that will be cast will be undergoing simple harmonic motion.

SHM phase, position, velocity, and acceleration

•  SHM can occur with various phase angles.

Dinosaurs, long tails, and the physical pendulum

•  The stride of Tyrannosaurus rex can be treated as a physical pendulum.

Damped oscillations

Forced (driven) oscillations and resonance

Forced (driven) oscillations and resonance II

•  The Tacoma Narrows Bridge suffered spectacular structural failure after absorbing too much resonant energy

Vocabulary: • Illumination=Işıklandırma • Abstract =Özet • Shine=Parlaklık • Flashlight =El feneri • Shadow = Gölge • Back and forth =İleri-Geri • Phase=Faz • Amplitude=Genlik • Stride =Adım • Damped oscillations=Sönümlü titreşimler • Driving force=itici güç • Undamped =Sönümsüz • Broaden=Genişletmek • Sharp=Keskin • Absorb =Emmek • Shift=Değişiklik • Artifical=Yapay • Forced oscillations=Zorla Salınımlar • Tendency=Eğilim • Apparatus=Cihaz, Malzeme

• Moduli=Modül • Equilibrium conditons=Denge koşulları • Tensile=Gerilme • Stress=Zor • Strain=Zorlanma • Attractive =Çekici • Sheer=Sapma • Angular distortion =Açısal Bozulma • Involve=İçermek • Solid inner core=Katı bir iç çekirdek • Molten outer core=Erimiş bir dış çekirdek • Mostly solid mantle= Çoğunlukla katı kabuk • Curved path= Kavisli yol • Straight path=Düz yol • Satellite Motion=Uydu hareketi • Orbit=Yörünge • Ordinary star=Sıradan bir yıldız • Accretion=Büyüme • Intense=Şiddetli • Simple harmonic motion=Basit harmonik hareket